Related papers: Stability criteria for q-expectation values
q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general,…
A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific…
The recent argue about the existence of an instability in the definition of the mean value appearing in the Tsallis non extensive Statistical Mechanic is reconsidered. Here, it is simply underlined that the pair of probability distributions…
A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
Based on the spectral decomposition technique, we introduce a simple and universal numerical method to analyze the stability of solitons. Adopting this method, the linear dynamical properties of $Q$-balls are systematically revealed, from…
We study the robustness of functionals of probability distributions such as the R\'enyi and nonadditive S_q entropies, as well as the q-expectation values under small variations of the distributions. We focus on three important types of…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
It is shown that the R\'enyi and Tsallis entropies and the q-expectation values, are continuous and stable if $q>1$ and are not continuous and instable for uniform finite distributions if $q<1$.
We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
We deal with the power-law q-distribution functions, so-called q-exponentials in nonextensive statistics. The system considered is a many-body Hamiltonian system with arbitrary interacting potentials. We find that the usual form of…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation valu of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort…
the stability criterion is constructed for open quantum systems which govern by quantum stochastic differential equations (QSDE) both for quantum observable flow and the stochastic density operator. We derive stability criteria (local,…
Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…
Usually the charge and the energy of stable Q-balls vary in a wide range or are even unbounded. In the present paper we study an interesting possibility that this range is parametrically small. In this case the spectra of stable Q-balls…
The class of $\alpha$-stable distributions is widely used in various applications, especially for modelling heavy-tailed data. Although the $\alpha$-stable distributions have been used in practice for many years, new methods for…